Investigation of the derivation and consistency of the quasi-two-dimensional flamelet models for non-premixed flames

Three non-premixed quasi-two-dimensional flamelet (Q2DF) models can be derived via integrating one-dimensional flamelet libraries, which are generated by premixing the third stream with the fuel stream or (and) the oxidizer stream as the premix fraction (eta) varied from zero to unity. These models are attractive and considered effective substitutes for two-dimensional flamelet (2DF) formulations; however, the connections between these Q2DF models and 2DF equations have not been clearly illustrated formerly. In this work, the 2DF formulations are converted from the space defined by two mixture fractions ( Z(1) x Z(2)) to that used for each Q2DF model ( xi x eta) in which xi designates a newly defined mixture fraction. For moderate Reynolds number conditions, it is considered that the Q2DF models and the 2DF formulations are equivalents as the one-dimensional (1D) flamelet elemental libraries are integrated upon sufficient grids of eta. To confirm this, the two-dimensional (2D) direct numerical simulations (DNS) and three-dimensional (3D) large-eddy simulation (LES) are performed to provide reference data since it is readily to associate the 2DF formulations with variable transports in physical space. The 2D DNS cases present various three-feed systems characterized by different third streams and ensure a well-mixed mixture in moderate eta, while the 3D LES case is performed with a large flux of pure CO2 as the third stream. Three Q2DF models are compared by using the same tracking parameters obtained from, respectively, the DNSs and LES. The comparisons based on the DNS cases demonstrate that the Q2DF models can reproduce the DNS data with quite satisfying accuracy, and it is confirmed that the accuracy has nothing to do with the type of the third stream. Through the LES results and the related comparisons, it can be concluded that the Q2DF models are reliable to predict the experimental measurements, and on the condition of a sufficient eta resolution, the three Q2DF models can give the same prediction in the whole range of eta.